# On a variational problem arising in crystallography

ESAIM: Control, Optimisation and Calculus of Variations (2007)

- Volume: 13, Issue: 1, page 72-92
- ISSN: 1292-8119

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topZaslavski, Alexander J.. "On a variational problem arising in crystallography ." ESAIM: Control, Optimisation and Calculus of Variations 13.1 (2007): 72-92. <http://eudml.org/doc/249925>.

@article{Zaslavski2007,

abstract = {
We study a variational problem which was introduced by Hannon,
Marcus and Mizel [ESAIM: COCV9 (2003) 145–149] to
describe step-terraces on surfaces of so-called “unorthodox” crystals.
We show that there is no nondegenerate intervals on which the absolute
value of a minimizer is $\pi/2$ identically.
},

author = {Zaslavski, Alexander J.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Minimizer; surfaces of crystals; unorthodox crystal;
variational problem.; variational problem.},

language = {eng},

month = {2},

number = {1},

pages = {72-92},

publisher = {EDP Sciences},

title = {On a variational problem arising in crystallography },

url = {http://eudml.org/doc/249925},

volume = {13},

year = {2007},

}

TY - JOUR

AU - Zaslavski, Alexander J.

TI - On a variational problem arising in crystallography

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2007/2//

PB - EDP Sciences

VL - 13

IS - 1

SP - 72

EP - 92

AB -
We study a variational problem which was introduced by Hannon,
Marcus and Mizel [ESAIM: COCV9 (2003) 145–149] to
describe step-terraces on surfaces of so-called “unorthodox” crystals.
We show that there is no nondegenerate intervals on which the absolute
value of a minimizer is $\pi/2$ identically.

LA - eng

KW - Minimizer; surfaces of crystals; unorthodox crystal;
variational problem.; variational problem.

UR - http://eudml.org/doc/249925

ER -

## References

top- B. Dacorogna and C.E. Pfister, Wulff theorem and best constant in Sobolev inequality. J. Math. Pures Appl.71 (1992) 97–118. Zbl0676.46031
- I. Fonseca, The Wulff theorem revisited. Proc. R. Soc. Lond. A432 (1991) 125–145. Zbl0725.49017
- J. Hannon, N.C. Bartelt, B.S. Swartzentruber, J.C. Hamilton and G.L. Kellogg, Step faceting at the (001) surface of boron doped silicon. Phys. Rev. Lett.79 (1997) 4226–4229.
- J. Hannon, M. Marcus and V.J. Mizel, A variational problem modelling behavior of unorthodox silicon crystals. ESAIM: COCV9 (2003) 145–149. Zbl1066.49011
- H.C. Jeng and E.D. Williams, Steps on surfaces: experiment and theory. Surface Science Reports34 (1999) 175–294.
- W.W. Mullins, Theory of thermal grooving. J. Appl. Physics28 (1957) 333–339.

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